Bell's Theorem and Negative Probabilities

[DrChinese]

1. I trust your follow-up will cover the QM prediction for cases in which the assumed distribution of $$\lambda$$ is not uniform.

2. The classical optics formula (i.e. the LR formula) is readily adapted, but can the QM one compete?

1. Why would I do that? The QM prediction does not need a $$\lambda$$. This is only present in LR.

2. As to your formula being the classical one... if it is the classical one, why is it at variance with Malus' Law?

The point is that Caroline's formula (1) is a late introduced formula which is essentially pulled from thin air, and can hardly be called classical in the normal sense of the term. And I would be very surprised to see an experiment demonstrate deviation from rotational invariance. Show me some significant references to these ideas prior to 1965.

Please note that EPR assumed rotational invariance, and also assumed that there was an angle at which there would be perfect correlation - something which does not occur at ANY angle with Caroline's formula (1).

 

[Hans de Vries]

3. So great, now we have a LR' prediction that satisfies Bell's Inequality. But it is significantly at variance with QM. And it does not match Malus' Law. Or experimental observation

Maybe I should let Caroline answer this but the formula is sound and
based on Malus law. It's not a coincidence that I came up with exactly
the same formula independently...

Etienne-Louis Malus proposed his optical law somewhere around 1810:
http://en.wikipedia.org/wiki/Etienne-Louis_Malus


The Malus law is used to derive:

$$A+B+ \ \ = \ \ \frac{1}{2\pi} \int^{+\pi}_{-\pi} \cos^2(\lambda-a) \cos^2(\lambda-b) d\lambda \ \ = \ \ \frac{1}{8} + \frac{1}{4} \cos^2(a-b)$$


First:

Normalized intensity after polarizer A is: $\cos^2(\lambda-a)$ (Malus Law)
Normalized intensity after polarizer B is: $\cos^2(\lambda-b)$ (Malus Law)

Going from optics to QM we presume that the photon detection rate
is proportional to the intensities after the polarizers.

We must multiply both photon rates to get the correlation of the
detections at A and B:

$$\cos^2(\lambda-a) \cos^2(\lambda-b)$$

This is the correlation for light with polarization angle lambda and
what rests is to integrate over all angles lambda.

Regards, Hans.

Malus Law:

http://scienceworld.wolfram.com/physics/MalussLaw.html
http://w3.ualg.pt/~jarod/geral/bibliote/phywe/2_5_04.pdf

 

[DrChinese]

Maybe I should let Caroline answer this but the formula is sound and
based on Malus law. It's not a coincidence that I came up with exactly
the same formula independently...

Hans, suddenly the light is going on about what you were discussing at your post #6, which I misread completely. As well as the posts immediately above this one, which I now see are related.

What you are talking about is a case in which the A and the B polarizers interact freely and locally with the hidden variable $$\lambda$$ and do not act entangled. So naturally when you have A=B the prediction is not perfect correlation at all.

OK, that is a fair discussion topic. Sorry that it took me so long to see where you were going with this whole classical thing. Ditto for Caroline and gptejms, my apologies for being so dense. I will now review the thread so I can comment more meaningfully.

(Clearly my application of the cos^2 law seemed reasonable to me, and matches the QM predictions and the Bell Inequality logic. And I can see where there is a difference in what we integrate - I put a constant where you are putting a variable in the integral. And clearly your formula leads to disagreement with experiment.)

 

[DrChinese]

Will the real classical correlation formula please stand up? Let's define our two contenders:

LR1: $$P(correlation)=cos^2\alpha$$ and entanglement is acknowledged
LR2: $$P(correlation)=.25+.5cos^2\alpha$$ and there is no entanglement

1. As I read EPR, LR1 is assumed. The possibility of using information gained at one location to learn more at another means a more complete specification of the system is possible. After all, the title of the paper is "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete" - and not "Can Quantum-Mechanical Description of Physical Reality Be Considered Accurate". I don't think the authors seriously questioned the predictive applications of QM.

In this view, the LR theorist explains the entangled correlation as follows: To the extent you ask the same question of entangled particles, you get the same answer. This allows the LR1 formula to mimic the QM predictions. The entanglement is real but the correlations are a logical consequence of yet-to-be-discovered hidden variables.

2. LR2, on the other hand, says that QM is simply wrong in its predictions. There is no entanglement; otherwise, there would be spooky action at a distance. The serious LR theorist might adopt this position because it is the only way to have complete independence of spatially separated measurements on hidden variables.

Both versions of LR state that the results of a measurement at one place do not affect the results of a measurement at another.

LR1 fails because of the Bell Theorem, which states that no LR can give all predictions the same as QM and be internally consistent.
LR2 fails because its predictions are statistically different than QM, and also outside the range of existing experimental tests.

Does this accurately portray the positions being discussed? (Caroline, I acknowledge that you don't agree about the experimental record.)

 

[gptejms]

In my post #29,I did a calculation for a pair of photons polarized at 90 degrees to each other---the question is, is such a state realizable in experiments?

Let me also add that the QM expectation value in this case would be $$-\cos(2 \alpha)$$ and not $$\cos(2 \alpha)$$.So the difference is really a factor of half.

 

[gptejms]

Here we are, I think it should be like this:

non-entangled photons according to QM: (arbitrary but equal polarization)

$$A+B+ \ \ = \ \ \frac{1}{2\pi} \int^{+\pi}_{-\pi} \cos^2(\lambda-a) \cos^2(\lambda-b) d\lambda \ \ = \ \ \frac{1}{8} + \frac{1}{4} \cos^2(a-b)$$


entangled photons according to QM:

$$A+B+ \ \ = \ \ \frac{1}{2\pi} \int^{+\pi}_{-\pi} \cos^2(\lambda-a) \cos^2(a-b) d\lambda \ \ = \ \ \frac{1}{2} \cos^2(a-b)$$

The only difference is that $(\lambda-b)$ becomes $(a-b)$ because the entanglement
assumes that the angle lambda becomes equal to a when the photon at
a is detected.

Regards, Hans

PS. lambda = polarization angle, a = angle of polarizator a, b = angle of polarizator b

I would rather look at the entangled case as follows.The factor (1/2) comes because of the prob. amplitude $$1/\sqrt 2$$ in the two photon state(see one of my posts on the last page).Once one photon shows up with say an x-polarization,the other also instantaneously gets to be in the same state of polarization and then has a probability $$\cos^2 (\alpha)$$ of passing thru the polarizer in its path.

 

[gptejms]

The general classical formula for correlated particles is, BTW:
$$P(a,b)=\int {d\lambda \rho (\lambda)p_a(\lambda )p_b(\lambda )}$$

The expressions discussed so far correspond to the special case in which all polarisation angles are equally probable and the assumptions are otherwise standard. They assume $$\rho (\lambda ) = constant$$ and $$p_a$$ and $$p_b$$ are both cosine functions. In many actual experiments, though, we don't have "rotational invariance", i.e. $$\rho (\lambda )$$ is not constant. A case of special interest is that when it is the sum of two delta functions, one centred on 0, the other on $$\pi$$, and $$\lambda$$ is a phase angle. [See http://arxiv.org/abs/quant-ph/9912082]

Caroline
http://freespace.virgin.net/ch.thompson1/

What makes you think that certain polarization angles are more likely than others?How do you decide these angles?

 

[Caroline Thompson]

Will the real classical correlation formula please stand up? Let's define our two contenders:

LR1: $$P(correlation)=cos^2\alpha$$ and entanglement is acknowledged
LR2: $$P(correlation)=.25+.5cos^2\alpha$$ and there is no entanglement

Hmmm ... but LR does not give just one formula for the correlation, it gives a method for calculating it! You can therefore get a range of different answers, corresponding approximately (after normalisation) to LR1, LR2 or any number of other formulae, so long as they have suitable properties such as correct periodicity.

As I pointed out in an earlier message, the general LR formula is:

$$P(a,b)=\int {d\lambda \rho (\lambda)p_a(\lambda )p_b(\lambda )}$$

The various functions depend on the exact experimental conditions. $$\rho$$ gives the probabilities of the different hidden variable values, whilst $$p_a$$ and $$p_b$$ give the probabilities of detection at the two detectors.

However, your description of the status quo is near enough correct. I have a slight quibble regarding what EPR actually believed, but that is not very relevant.

Cheers
Caroline

 

[Hans de Vries]

I would rather look at the entangled case as follows.The factor (1/2) comes because of the prob. amplitude $$1/\sqrt 2$$ in the two photon state(see one of my posts on the last page).Once one photon shows up with say an x-polarization,the other also instantaneously gets to be in the same state of polarization and then has a probability $$\cos^2 (\alpha)$$ of passing thru the polarizer in its path.

A remark:

I see a conflict here between Relativistic Quantum Mechanics
and the Non-Relativistic Born Probabilistic interpretation of QM
which is used by the Teleportation proponents. (The Born
interpretation can be studied in Robert B. Griffiths' book:
Consistent Quantum Theory)


Relativistic Quantum Mechanics states that photons are particles
with spin 1 and that a photon has either a spin up or a spin down in
the direction of motion. This corresponds with left and right circular
polarization.

Linear polarized single photons can not exist as fundamental photons
since they would be of spin 0. Linear polarized photons would be a
combination of a spin up and a spin down photon with the phase
relation determining the polarization angle.

Regards, Hans

(This actually opens an interesting loophole that allows to interpret the
results of the Aspect and Innsbruck experiments in a fashion that
respects the locality of Special Relativity, see a post somewhere in
the near future)

 

[DrChinese]

I think this comes pretty close to putting the formulas on equal footing in language that should be consistent with what we have been expressing:

The LR1 (entangled) prediction is:

$$P(+,+) = \int .5 \cos^2(\lambda-\alpha) \cos^2(\lambda-\beta) d\phi$$

and the right side reduces to the same $$.5 \cos^2 (\alpha-\beta)$$ as previous.

The LR2 (non-entangled) prediction is:

$$P(+,+) = \int \cos^2(\lambda)\cos^2(\lambda-\alpha) \cos^2(\lambda-\beta) d\phi$$

and the right side reduces to the same $$.125 + .25\cos^2 (\alpha-\beta)$$ as previous (I didn't work it out myself but I trust it is fine).

This allows us to easily see the term that accounts for the difference in the results. As Caroline and others have stated, conceptually the basic cos^2 formula - or others - could be re-arranged in other permutations. Presumably, the point of that exercise would be to demonstrate possible predictive functions which could be compared to experimental results and which supported LR.

So that leaves us again with the same kind of problems with LR theories, namely either:

1. They give identical predictive results as QM (as the LR1 theory does) but fails to clear the hurdle of Bell's Theorem; or
2. They satisfy Bell's Theorem (as the LR2 theory does), but are nowhere close to any experimental tests performed to date.

You have to admit that the perfectly correlated case is enough to blow LR2 out of the water by itself. If QM predicts 100% correlation, and LR2 predicts 75% correlation, and experiment is around 99%... well, how do you begin to rescue such a theory? And why do you try? I mean, the correlated case completely goes against the grain of the LR2 concept of complete local independence at the polarizers. If LR2 was even close to correct, this is the one place you would expect it to hit its mark.

Anyway, this is the beauty of Bell's Theorem. It creates a rather large divide between QM and all possible LR theory applications, allowing experimental results to select between them.

 

[Caroline Thompson]

I think this comes pretty close to putting the formulas on equal footing in language that should be consistent with what we have been expressing:

The LR1 (entangled) prediction is:

$$P(+,+) = \int .5 \cos^2(\lambda-\alpha) \cos^2(\lambda-\beta) d\phi$$

and the right side reduces to the same $$.5 \cos^2 (\alpha-\beta)$$ as previous.

But it doesn't! See the detailed working in Appendix C of http://arxiv.org/abs/quant-ph/9903066. Or am I missing something?

Anyway, I don't see how it can come to anything other than your LR2 solution, $$.125 + .25\cos^2 (\alpha-\beta)$$ .

... As Caroline and others have stated, conceptually the basic cos^2 formula - or others - could be re-arranged in other permutations. Presumably, the point of that exercise would be to demonstrate possible predictive functions which could be compared to experimental results and which supported LR.

Yes, the point is to enable comparison with actual experiments, but what is involved is rather more than a rearranging of the cos^2 terms. We completely replace them by other functions, perhaps obtained empirically in subsidiary experiments.

Why not go back to the general LR formula instead of thinking in terms of epicycles added onto the cos^2 one?

So that leaves us again with the same kind of problems with LR theories, namely either:

1. They give identical predictive results as QM (as the LR1 theory does) but fails to clear the hurdle of Bell's Theorem; or
2. They satisfy Bell's Theorem (as the LR2 theory does), but are nowhere close to any experimental tests performed to date.

Ah well, we have to agree to differ here. Under my interpretation of the experiments, the various "loopholes" mean that none is actually in conflict with the general LR formula and all are compatible with "valid" versions of Bell's inequality. [Most, if not all, tests use versions that not valid, in the sense of not being able to discriminate between LR and QM, because they rely on supplementary assumptions that are, from a LR points of view, most unlikely to be true.]

You have to admit that the perfectly correlated case is enough to blow LR2 out of the water by itself. If QM predicts 100% correlation, and LR2 predicts 75% correlation, and experiment is around 99%... well, how do you begin to rescue such a theory?

You rescue it by looking carefully at the facts! Where do you get that figure of 99% from? In real optical experiments it must be remembered that only a small fraction of the "photons" are detected. Actual frequencies of coincidences tend to be of the order of less than 1%. The only Bell test experiment I know of in which correlations really were that high has been the Rowe et al one, using trapped ions. This, though, can scarcely be taken seriously, since the ions were by no means physically independent. The two "photons" were not even measured independently. [See http://en.wikipedia.org/wiki/Bell_test_loopholes ]

I know you have said that the subject is to be discussed on the basis of the assumed agreement of experiments with QM, but I really can't see how this makes scientific sense! First prove that agreement, then it will be worthwhile interpreting the consequences.

And why do you try? I mean, the correlated case completely goes against the grain of the LR2 concept of complete local independence at the polarizers. If LR2 was even close to correct, this is the one place you would expect it to hit its mark.

Can you tell us what particular experiment you had in mind, with this 99% correlation?

Cheers
Caroline

 

[DrChinese]

1. But it doesn't! See the detailed working in Appendix C of http://arxiv.org/abs/quant-ph/9903066. Or am I missing something?

2. Yes, the point is to enable comparison with actual experiments, but what is involved is rather more than a rearranging of the cos^2 terms. We completely replace them by other functions, perhaps obtained empirically in subsidiary experiments.

3 Ah well, we have to agree to differ here. Under my interpretation of the experiments, the various "loopholes" mean that none is actually in conflict with the general LR formula and all are compatible with "valid" versions of Bell's inequality. [Most, if not all, tests use versions that not valid, in the sense of not being able to discriminate between LR and QM, because they rely on supplementary assumptions that are, from a LR points of view, most unlikely to be true.]

You rescue it by looking carefully at the facts! Where do you get that figure of 99% from?

Cheers
Caroline

1. You derivation looks as identical as it gets, so I guess I set it up wrong. I'll see if I can do better. It doesn't change anything because the result is still as I have it, which is p(LR1)=p(QM) in the end. By definition, that is what Bell is working toward... LR giving identical predictions to QM.

2. Yes, well adjusting theory after conducting experiments is a great activity. Why don't you try it some time? Your theory shifts with the wind, but is never responsive to the experimental record... because you don't want it to.

If you showed me a suitable experiment, I would abandon my beliefs tomorrow. I am not married to the position so much that I couldn't change it. But that is not true for you, is it?

3. And just to make it clear who looks at the facts and who doesn't, let's see if I understand it correctly:

Author A publishes in a respected, peer reviewed physics journal than the predictions of QM are confirmed to 5 standard deviations. You ignore the result, and interpret that as evidence that your alternate predictions are actually correct.

Author B publishes in a respected, peer reviewed physics journal than the predictions of QM are confirmed to 10 standard deviations. You ignore the result, and interpret that as evidence that your alternate predictions are actually correct.

Author C publishes in a respected, peer reviewed physics journal than the predictions of QM are confirmed to 30 standard deviations. You ignore the result, and interpret that as evidence that your alternate predictions are actually correct.

Is there a pattern here? There have been any number of tests of entangled correlation and they all say the exact same thing. And you deny them all.

So as to what experiment I am referring to... any and all because they all say the same thing. Aspect, Dalibard, Grangier, Physical Review Letters, 1982, p 1807. Each case the figures are in terms of the actual published results, which are usually expressed in terms of the actual experimental setup and not the underlying cos^2 formula directly as you know:

S(Experimental)=.101 +/-.020 (that would be the range .081 to .121)
S(QM)=.112 (that would be neatly inside the observed range)
S(LR per Bell Inequality)<=.0000 (that would be far outside the observed range)
(For the 22.5/67.5 degrees case)

Figure 4, same paper: A graph of the key angles 0, 22.5, 45, 67.5 and 90 degrees settings (the only ones shown, same ones I have tried to emphasize for our discussions) indicates perfect agreement between the QM predicted cos^2 function and experimental results. As you have acknowledged, this is substantially different than the LR2 predictions you have put forth.

For coincidence rates: At the 0 degree setting, the result is almost to the penny 100% of the expected count per QM. At the 90 degrees setting, the result is almost exactly 0. Both of these results are wildly at variance with the LR2 result which would be 75% at 0 degrees and 25% at 90 degrees.

I know you think these results are flawed, but: a) the rest of the scientific community accepts the results, even those that have questions about "loopholes"; and b) nothing about the results even remotely supports the LR2 position or anything close to it.

So when we are working on theory construction, you must either consider logic and evidence or not; and you are saying you will not. Nothing you say erases the paradox of LR1 and LR2 I have shown above. Your hypothesis is not credible in this light. I would advise you to construct an LR theory that matches experiment and doesn't violate Bell, but we can see that is not feasible.

 

[Caroline Thompson]

If you showed me a suitable experiment, I would abandon my beliefs tomorrow ...

The extensions of Grangier's latest proposal for a loophole-free experiment (see Sanchez et al paper) that I suggest in http://freespace.virgin.net/ch.thompson1/Papers/Homodyne/homodyne.htm would be useful start.

I am not married to the position so much that I couldn't change it. But that is not true for you, is it?

True! Local realism is, after all, "reality"! It would take a lot more than a few imperfect experiments to shake by belief in this.

3. And just to make it clear who looks at the facts and who doesn't, let's see if I understand it correctly:

Author A publishes in a respected, peer reviewed physics journal than the predictions of QM are confirmed to 5 standard deviations. You ignore the result, and interpret that as evidence that your alternate predictions are actually correct.

No, I go away and read the actual published papers, look up refs from them, write to the experimenters concerned, get hold sometimes of copies of their PhD theses (in the case of Aspect, this is in French and took me a considerable effort to read, but I've read every one of the 400-odd pages!). I don't ignore the results, I simply find alternative explanations. I have the advantage of an initially completely open mind as to how these explanations should work, apart from a preference for those that make physical sense, i.e. are local and explain the physical causes.

Author B publishes in a respected, peer reviewed physics journal than the predictions of QM are confirmed to 10 standard deviations. You ignore the result, and interpret that as evidence that your alternate predictions are actually correct.

[Could it be that people employed to do quantum physics have an exaggerated respect for the other quantum physicists who make up the editorial boards etc of the said journals?]

So as to what experiment I am referring to... any and all because they all say the same thing. Aspect, Dalibard, Grangier, Physical Review Letters, 1982, p 1807. Each case the figures are in terms of the actual published results ...

Yes, but this is only after subtraction of accidentals. The raw data would have been (judging by the results from a similar experiment of Aspect et al's -- see http://arxiv.org/abs/quant-ph/9903066) nearer to the basic local realist prediction and not in violation of the CH74 Bell test that he used.

... I know you think these results are flawed, but: a) the rest of the scientific community accepts the results, even those that have questions about "loopholes"; and b) nothing about the results even remotely supports the LR2 position or anything close to it.

See above ref to my paper.

I would advise you to construct an LR theory that matches experiment and doesn't violate Bell, but we can see that is not feasible.

But that is precisely what I have done. LR theory matches experiment but does not exactly match the QM prediction!

Caroline

 

[DrChinese]

1. [Could it be that people employed to do quantum physics have an exaggerated respect for the other quantum physicists who make up the editorial boards etc of the said journals?]

2. Yes, but this is only after subtraction of accidentals. The raw data would have been (judging by the results from a similar experiment of Aspect et al's -- see http://arxiv.org/abs/quant-ph/9903066) nearer to the basic local realist prediction and not in violation of the CH74 Bell test that he used.

1. Gee, I guess the status quo is all that gets published. But if that were so, why would they bother publish any journals at all? After all, they know it all... Or maybe your comment is a actually measure of your frustration that the scientific community has not embraced your ideas.

2. Subtraction of accidentals, yes, accepted by the scientific community but not you. As well as the hypothetical existence of loopholes that distort the results.

So let's get specific here, Caroline. Considering correlation percentages at various angles (from above posts):

P(QM,22.5)=.8536
P(LR, 22.5)=.6768

and you assert that:
P(Experiment, 22.5)=P(loopholes,22.5)+P(LR,22.5)

Therefore by your logic:
P(loopholes,22.5)=.1768

a. Please supply any predictive formula (and specific theoretical support) for P(loopholes) such that P(Experiment, $$\theta$$)=P(loopholes,$$\theta$$)+P(LR, $$\theta$$) for all $$\theta$$. Please do not cite papers such as your Chaotic Ball models that simply say such a mechanism could exist without providing a specific framework for a specific value that fits this criteria.

b. Alternately, cite any published experiment which itself purports to identify and measure the actual values of P(loopholes). Please do not cite experiments in which the authors themselves do not claim such a value has been measured.

You assert the experimental results are flawed: now show how this flaw justifies your LR predictions to the exclusion of all other predictions. After all, how do we know that P(loopholes) is not actually close to zero? That is certainly a reasonable outcome from the perspective of objective observers who acknowledge loopholes! There is no reason to assume that plugging loopholes will actually lead to any different net results than have already been published for Bell tests.

 

[Caroline Thompson]

1. Gee, I guess the status quo is all that gets published. But if that were so, why would they bother publish any journals at all? ...

Hmmm ... I sometimes wonder! It seems easy enough to publish new experimental results, but new interpretations of experiments are a different matter.

2. Subtraction of accidentals, yes, accepted by the scientific community but not you. As well as the hypothetical existence of loopholes that distort the results.

Not so, when it comes to Bell test experiments. The Geneva group, who published only the Bell test based on adjusted data in 1998 for their first "long-distance" Bell test, published results with and without adjustment in later papers. The reason? I had had some communication with Gisin on the subject, and met him at a conference.

Nobody has ever challenged my argument. Though Aspect defended the subtraction in 1985 after Marshall et al had challenged it, he never responded to my letters.

Incidentally, in most experiments subtraction of accidentals does not matter, so long as it is done consistently. It is possibly only in Bell tests that it causes bias, increasing test statistics.

So let's get specific here, Caroline. Considering correlation percentages at various angles (from above posts):

P(QM,22.5)=.8536
P(LR, 22.5)=.6768

and you assert that:
P(Experiment, 22.5)=P(loopholes,22.5)+P(LR,22.5)

Therefore by your logic:
P(loopholes,22.5)=.1768

I don't understand your notation. Why not look instead at the data in my paper, http://arxiv.org/abs/quant-ph/9903066? The idea that you can produce a meaningful general formula for the probability of loopholes causing a given bias does not make sense. Every experiment is different.

... how do we know that P(loopholes) is not actually close to zero?

Take it or leave it, DrChinese! I merely report what I believe to be the facts.

There is no reason to assume that plugging loopholes will actually lead to any different net results than have already been published for Bell tests.

This is simply not true! In the case of the subtraction of accidentals, my re-analysis of Aspect's and Tittel's experiments covered in the above paper (quant-ph/9903066) already demonstrates this.

In the case of the detection loophole, it is a matter of logic together with physical plausibiliy. If we're dealing with spin-1/2 particles, the logic is covered in my Chaotic Ball model. If dealing with light, we're best off looking at the problem algebraically. It's not quite so intuitively obvious why the loophole is open, since you can, under the usual assumptions of classical wave theory, get both +1 and -1 results at once. The argument is that in reality instrumenst don't perform quite as assumed under standard classical theory, with the result that occurrences of both +1 and -1 at once are much less frequent than the basic theory predicts.

Cheers
Caroline
http://freespace.virgin.net/ch.thompson1/

 

[DrChinese]

The idea that you can produce a meaningful general formula for the probability of loopholes causing a given bias does not make sense. Every experiment is different.

...Take it or leave it, DrChinese! I merely report what I believe to be the facts.

You aren't reporting any facts, and that is my point. You acknowledge that every experiment is different and yet they all produce exactly the same results - i.e. exactly the same amount of bias and error! How can this be if you are right? If you were right, there would be an exact formula that yields precisely the difference between observation and prediction by LR - at every angle. We could then come to understand the reason for it. But there is no such experimental bias - repeatable loopholes that always affect measurements in exactly the same way regardless of experimental setup! That is why you cannot get from here to there.

It is not science to throw out repeatable experiments and put nothing better in its place. Your logic is wiggling like jello. Make a specific prediction, and specifically explain experimental bias and you have something.

 

[Caroline Thompson]

You aren't reporting any facts, and that is my point. You acknowledge that every experiment is different and yet they all produce exactly the same results - i.e. exactly the same amount of bias and error!

They don't all have the same bias! They start from situations that have varying natural (hidden variable) correlations, then the experimenters select from among the various trial runs those conditions that produce "good strong correlations". Local realist theories and QM agree about the general shape of the correlation curve. It is, to a good approximation, sinusoidal. [NB if you read that it is a zig-zag you are behind the times: it is universally recognised that for optical tests the LR prediction is a sine curve.] They disagree only in the value of a constant term: zero under QM, positive under the basic LR theory.

I'm getting tired of this discussion, though, in which you endlessly criticize my conclusions without showing any sign of having read and understood my various papers. Have you actually tried to understand them? I can't personally see how it is possible to be aware of the various loopholes and yet bury your head in the sand and say you believe that they are unimportant -- that, in spite of them, it is QM that is correct, LR ruled out.

It is not science to throw out repeatable experiments and put nothing better in its place. Your logic is wiggling like jello. Make a specific prediction, and specifically explain experimental bias and you have something.

Local realists have predicted since 1970 that increasing quantum efficiency in an optical Bell test will, other things being equal, result in decreased values of the CHSH test statistic. If you want to argue your case, first find me evidence that this is not so! Persuade an experimenter to put it to the test.

We can also (as you must have realized by now) show that if you subtract accidentals you inevitably increase all the various Bell test statistics.

It is the Bell tests that count, not the numerical agreements of "normalised" coincidence rates.

Caroline
http://freespace.virgin.net/ch.thompson1/

 

[DrChinese]

1. They don't all have the same bias! They start from situations that have varying natural (hidden variable) correlations, then the experimenters select from among the various trial runs those conditions that produce "good strong correlations". Local realist theories and QM agree about the general shape of the correlation curve. It is, to a good approximation, sinusoidal. [NB if you read that it is a zig-zag you are behind the times: it is universally recognised that for optical tests the LR prediction is a sine curve.] They disagree only in the value of a constant term: zero under QM, positive under the basic LR theory.

2. I'm getting tired of this discussion, though, in which you endlessly criticize my conclusions without showing any sign of having read and understood my various papers. Have you actually tried to understand them? I can't personally see how it is possible to be aware of the various loopholes and yet bury your head in the sand and say you believe that they are unimportant -- that, in spite of them, it is QM that is correct, LR ruled out.

1. That is my point. There is no mathematical way that a bias can occur on every variant of the EPR tests and always come back to the QM prediction. If the QM prediction had nothing to do with anything, then some experiments would yield different values from the QM prediction - presumably closer to the LR formula you push sometimes. But that doesn't happen. 100% of the authors of EPR test papers report that the QM predictions are in the range of their results. You have never put forth an argument that you can quantify the loopholes; and then show that the net amount of those loopholes leads to the LR predicitons.

You say that QM and LR agree on the general shape of the curve? That is a laugh, because the predictions are miles apart at certain angles, such as 0 and 90 degrees where they differ radically.

2. You are tired? I guess that door swings both ways. I have reviewed the chaotic ball paper and you ought to be ashamed to cite it. It doesn't say anything more than: Maybe this, maybe that. You have done a lot better work than that.

I have asked for evidence, not speculation. We can speculate that a man did not walk on the moon, but there is plenty of evidence that he did.

Meanwhile, here is an example of the published record that you blow off at the drop of a hat:

Aspect, Physical Review Letters, 1981, peer reviewed: "As a conclusion, our results, in excellent agreement with quantum mechanics predictions, are to a high statistical accuracy a strong evidence again the whole class of realistic local theories;..."